OFFSET
1,2
COMMENTS
LINKS
Luc Ta, Table of n, a(n) for n = 1..14
K. Hong, H. Lee, H. J. Lee and S. Oh, Small knot mosaics and partition matrices, J. Phys. A: Math. Theor. 47 (2014) 435201; arXiv:1312.4009 [math.GT].
K. Hong, H. J. Lee, H. Lee and S. Oh, Upper bound on the total number of knot n-mosaics, J. Knot Theory Ramifications, Volume 23, Issue 13, November 2014; arXiv:1303.7044 [math.GT].
Hwa Jeong Lee, Kyungpyo Hong, Ho Lee, and Seungsang Oh, Mosaic number of knots, arXiv: 1301.6041 [math.GT], 2014.
Samuel J. Lomonaco and Louis H. Kauffman, Quantum Knots and Mosaics, Proc. Sympos. Applied Math., Amer. Math. Soc., Vol. 68 (2010), pp. 177-208.
Samuel J. Lomonaco and Louis H. Kauffman, Illustration for a(3) = 22, from "Quantum Knots and Mosaics", 2010, with permission.
Seungsang Oh, Kyungpyo Hong, Ho Lee, and Hwa Jeong Lee, Quantum knots and the number of knot mosaics, arXiv: 1412.4460 [math.GT], 2014.
MATHEMATICA
x[0] = o[0] = {{1}};
x[n_] := ArrayFlatten[{{x[n - 1], o[n - 1]}, {o[n - 1], x[n - 1]}}];
o[n_] := ArrayFlatten[{{o[n - 1], x[n - 1]}, {x[n - 1], 4*o[n - 1]}}];
mosaicsSquare[n_] := If[n > 1, 2*Total[MatrixPower[x[n - 2] + o[n - 2], n - 2], 2], 1];
Flatten[ParallelTable[mosaicsSquare[n], {n, 1, 11}]] (* This program is based on Theorem 1 of Oh, Hong, Lee, and Lee (see Links). - Luc Ta, Aug 13 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 18 2015
EXTENSIONS
a(7)-a(11) from Hiroaki Yamanouchi, Aug 19 2015
Typo in a(11) corrected by Luc Ta, Aug 13 2024
STATUS
approved